Problem: Simplify the following expression: $p = \dfrac{-88x^3}{55x^3 + 143x^2}$ You can assume $x \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-88x^3 = - (2\cdot2\cdot2\cdot11 \cdot x \cdot x \cdot x)$ The denominator can be factored: $55x^3 + 143x^2 = (5\cdot11 \cdot x \cdot x \cdot x) + (11\cdot13 \cdot x \cdot x)$ The greatest common factor of all the terms is $11x^2$ Factoring out $11x^2$ gives us: $p = \dfrac{(11x^2)(-8x)}{(11x^2)(5x + 13)}$ Dividing both the numerator and denominator by $11x^2$ gives: $p = \dfrac{-8x}{5x + 13}$